Due: Wednesday, 5/21 (Presentations begin on 5/20)
Objective: to research an important figure in the history of mathematics.
Project: You will choose a famous mathematician. You will write a short (2 to 3 page) research paper about this mathematician and then present your findings to the class. Your paper should contain the following:
A.) biographical information about your mathematician B.) any significant contributions by this figure to the field of mathematics C.)any interesting controversies, conflicts or anecdotes surrounding your mathematician D.)a description of how your mathematician’s contributions are still relevant to the field today.
Requirements:
A.) Your paper must be typewritten, double spaced and 12 pt. font.
B.) You must have at least 3 references (internet resources are okay). Include a bibliography.
C.) DO NOT plagiarize. Any information or quotes should cite the source in some way (footnotes, etc.).
Period 6 - BC Calc - Calendar of Activities Click on the activities for details. Where applicable, handouts are uploaded as attachments.
Today we studied the Direct and Limit Comparison tests. For homework students should complete the problems from the "Mass Insight" packet on the Comparison Tests.
Today we learned about Volumes of Solids with Known Cross Sections, better known as the "slicing" method. Student were given a problem set which is due on Tuesday, 2/4.
2nd Quarter Project - Due Tue 12/3: Create an illustration / example for one of the concepts / vocab terms that we've learned. Do this on 8.5 x 11 inch paper. I will post these on my bulletin board and on my wall. Make the topic or term very clear. Think of it as a "mini poster". Be creative and have fun with it!
Here is the Rubric that I will use to score the project.
Click Here for the College Board website (Calc AB Section).
For homework, students should finish the free response questions 2000 AB 3 and score it. We'll go over the scoring guide tomorrow.
Today we learned about Concavity and Curve sketching. Students graphed functions using first and second derivatives, increasing/decreasing and concavity behavior.
For those who were absent, the procedure is as follows:
1.) Find the zeros of the function
2.) Find f'(x) and discover where it equals zero and/or doesn't exist - These are your Critical Points.
3.) Find f''(x) and discover where it equals zero and/or doesn't exist - These are your Possible Inflection Points.
4.) Map out the where f'(x) and f''(x) are positive and negative on sign charts.
5.) Make a table of values with your zeros, critical points, inflection points and end points (if any).
6.) Graph the points, then sketch the curve using the derivatives to indicate increasing/decreasing behavior and concavity.
For homework, students should finish graphing the function f(x) = 3x^(4/3) - 12x^(1/3) on [- infinity , infinity]. The video below on "Graphing Using Derivatives" should help.
Here are the links to the videos from the day's when I was out:
You may also want to check out some of the Khan Academy videos on this topic. I will put the link on the Wiki, but they can be found at: Click here to be brought to those videos.
On Friday, students learned the process for identifying local and absolute extreme values of functions and how to justify these ideas. Here is a screen shot of the "special cases" function which I discussed with notes added.
End of Year Mathematicians Project
Today I assigned the Mathematicians Project. It will be scored using this rubric.
See below for more information:
Calculus – 4th Quarter Project
Due: Wednesday, 5/21 (Presentations begin on 5/20)
Objective: to research an important figure in the history of mathematics.
Project: You will choose a famous mathematician. You will write a short (2 to 3 page) research paper about this mathematician and then present your findings to the class. Your paper should contain the following:
A.) biographical information about your mathematician
B.) any significant contributions by this figure to the field of mathematics
C.)any interesting controversies, conflicts or anecdotes surrounding your mathematician
D.)a description of how your mathematician’s contributions are still relevant to the field today.
Requirements:
A.) Your paper must be typewritten, double spaced and 12 pt. font.
B.) You must have at least 3 references (internet resources are okay). Include a bibliography.
C.) DO NOT plagiarize. Any information or quotes should cite the source in some way (footnotes, etc.).
Period 6 - BC Calc - Calendar of Activities
Click on the activities for details. Where applicable, handouts are uploaded as attachments.
Old Stuff
Homework for tomorrow:
1.) Complete the AP Problems from the Power Series Handout
2.) Finish verifying these four derivatives using MacLaurin Series
3.) Memorize the four important MacLaurin Series for a quick quiz tomorrow.
Integral Test 1
Integral Test 2
Integral Test 3
Integral Test 4
Integral Test 5
Integral Test 6
Today we studied the Direct and Limit Comparison tests. For homework students should complete the problems from the "Mass Insight" packet on the Comparison Tests.
I handed out the Problem Set Infinite Series, which will be due next Thursday.
You will also have a test next Thursday, 3/27
Your Test Corrections for the Diff-E-Q, Parametric and Polar Function Test will be due next Friday, 3/28.
February Break Assignment - Parametrics Packet
Daily Notes -Wednesday, Feb 12, 2014.
Today we went over the material from "Assignment 2 - Differential Equations and the AP Exam" (See Below).
For Friday, students should work on completing 2005 AB6 and 2006 (Form b) AB 5
Assignment 1 - AP Free Response Questions - Integration by Parts and Average Value
Assignment 2 - Differential Equations and the AP Exam - Read and mark-up the handout. There are two problems at the end to try out. We'll go over this on Wednesday in class.
I will check these when I see you on Wednesday.
Today we learned about Volumes of Solids with Known Cross Sections, better known as the "slicing" method. Student were given a problem set which is due on Tuesday, 2/4.
Click here for Problem Set 11.
Here are some screen shots from class to help you with the method:
Here is the formula to use for volumes of cross sections
Here are the steps to follow
Here are the initial steps for Set up
Here is the set up of the integral
Here is the evaluation of the integral
Today we continued working on Integration by Parts, then moved onto the method of Partial Fractions
Midterm Review Info:
Midterm Topic List
Midterm Review Packet
For Tuesday, complete Problem Set 10 - Special Integration Techniques
More review materials:
Midterm Review #1 - Limits and Continuity
Midterm Review #2 - Definition of derivative
Midterm Review #3 - Derivative formulas
Midterm Review #4 - Curve Sketching
Midterm Review #5 - Riemann Sums
Midterm Review #6 - Antiderivatives
The midterm will be made of:
10 Multiple Choice - non-Calculator
1 Free Response - non-Calculator
10 Multiple choice - Calculator Active
1 Free Response - Calculator Active
I will hand out topic list in class.
Materials for Integration by parts:
Example problem
Classwork Problems
Worked out Solutions to 1 and 2
Worked out Solutions to 3
AP Exam Questions Integration by Parts handout
1.) Integration by substitution assignment:
a.) "Substitution in Indefinite Integrals" - p. 333-334, Through EXAMPLE 5 ONLY
b.) "Substitution in Definite Integrals" - p. 336-337
Do the following Exercises: p. 338, # 17 - 19, 25 - 27 and 53 - 55
2.) Antidifferentiation by Parts Reading
Read p. 341 - 344 and be prepared to discuss "Integration by Parts" on Monday and watch a video from Khan Academy on Integration by parts.
2nd Quarter Project - Due Tue 12/3: Create an illustration / example for one of the concepts / vocab terms that we've learned. Do this on 8.5 x 11 inch paper. I will post these on my bulletin board and on my wall. Make the topic or term very clear. Think of it as a "mini poster". Be creative and have fun with it!
Here is the Rubric that I will use to score the project.
Click Here for the College Board website (Calc AB Section).
For homework, students should finish the free response questions 2000 AB 3 and score it. We'll go over the scoring guide tomorrow.
Today we learned about Concavity and Curve sketching. Students graphed functions using first and second derivatives, increasing/decreasing and concavity behavior.
For those who were absent, the procedure is as follows:
1.) Find the zeros of the function
2.) Find f'(x) and discover where it equals zero and/or doesn't exist - These are your Critical Points.
3.) Find f''(x) and discover where it equals zero and/or doesn't exist - These are your Possible Inflection Points.
4.) Map out the where f'(x) and f''(x) are positive and negative on sign charts.
5.) Make a table of values with your zeros, critical points, inflection points and end points (if any).
6.) Graph the points, then sketch the curve using the derivatives to indicate increasing/decreasing behavior and concavity.
For homework, students should finish graphing the function f(x) = 3x^(4/3) - 12x^(1/3) on [- infinity , infinity]. The video below on "Graphing Using Derivatives" should help.
Here are the links to the videos from the day's when I was out:
Concavity, concave upwards and concave downwards intervals
Exercises: Recognizing Concavity
Inflection points
Graphing using derivatives
From Thursday: Please complete the BC Calculus Motion Problems for next week.
You may also want to check out some of the Khan Academy videos on this topic. I will put the link on the Wiki, but they can be found at: Click here to be brought to those videos.
Monday we learned about the Mean Value Theorem. You can access the guided notes here. There was also a Powerpoint Presentation.
On Friday, students learned the process for identifying local and absolute extreme values of functions and how to justify these ideas. Here is a screen shot of the "special cases" function which I discussed with notes added.
Halloween Activity
Students completed 1998 BC 78, a related rates problem for a Ticket to Leave. The solution to that can be found here.
From Monday:
Click here for a screen shot of a linear approximation problem.
Click here for 1997 BC 23, a related rates problem. Here is a worked out solution to this problem. However, the green didn't show up to well.
Here are some screenshots of the problems from the "Related Rates - Guided Notetaking packet:
Click here for Page 1 - #'s 1 and 2
Click here for Page 2 - #'s 3 and 4
From last week:
Last week we solved the Ladder Problem, which you will find marked up if you click the link.
The procedure for solving these problems can be found if you click here.
I handed back the derivatives test yesterday. Test corrections will be due on Monday, 10/28: Click her for the Test Corrections Procedure
Yesterday we also reviewed the Implicit Diff Handout. Here are some screen shots:
Problems 1 - 5 from the Implicit Differentiation packet. Here are some pictures:
Problem 1 Problem 2 Problem 3 Problem 4 Problem 5
Here are some screen shots of the multiple choice problems from the packet:
1997 AB 17
1998 AB 6
2003 AB 26
2008 AB 16
The free response questions can be found at the AP Central website, here